If in negative they are used, then would the sentence like He asked me, "Why don't you work?". be transformed as He asked me why I didn't work. ?
– Sarthak123Feb 23 '16 at 13:49

@Sarthak123 Yes but the backshift is not necessary if the time is clear. You can either say he asked me why I don't work or he asked my why I didn't work. But in this case, the negative is required just to invoke the auxiliary don't.
– AlejandroFeb 23 '16 at 14:29